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Simplifying 4b + -5 + (-1a + -3) * i = 7 + -81 Reorder the terms: 4b + -5 + (-3 + -1a) * i = 7 + -81 Reorder the terms for easier multiplication: 4b + -5 + i(-3 + -1a) = 7 + -81 4b + -5 + (-3 * i + -1a * i) = 7 + -81 Reorder the terms: 4b + -5 + (-1ai + -3i) = 7 + -81 4b + -5 + (-1ai + -3i) = 7 + -81 Reorder the terms: -5 + -1ai + 4b + -3i = 7 + -81 Combine like terms: 7 + -81 = -74 -5 + -1ai + 4b + -3i = -74 Solving -5 + -1ai + 4b + -3i = -74 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -1ai + 4b + 5 + -3i = -74 + 5 Reorder the terms: -5 + 5 + -1ai + 4b + -3i = -74 + 5 Combine like terms: -5 + 5 = 0 0 + -1ai + 4b + -3i = -74 + 5 -1ai + 4b + -3i = -74 + 5 Combine like terms: -74 + 5 = -69 -1ai + 4b + -3i = -69 Add '-4b' to each side of the equation. -1ai + 4b + -4b + -3i = -69 + -4b Combine like terms: 4b + -4b = 0 -1ai + 0 + -3i = -69 + -4b -1ai + -3i = -69 + -4b Add '3i' to each side of the equation. -1ai + -3i + 3i = -69 + -4b + 3i Combine like terms: -3i + 3i = 0 -1ai + 0 = -69 + -4b + 3i -1ai = -69 + -4b + 3i Divide each side by '-1i'. a = 69i-1 + 4bi-1 + -3 Simplifying a = 69i-1 + 4bi-1 + -3 Reorder the terms: a = -3 + 4bi-1 + 69i-1
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